Question

Wo children (m = 33.0 kg each) stand opposite each other on the edge of a merry-go-round. the merry-go-round, which has a mass of 1.66 ✕ 102 kg and a radius of 1.2 m, is spinning at a constant rate of 0.46 rev/s. treat the two children and the merry-go-round as a system.

Answer 1

The conservation of angular momentum principle is used to find the new angular velocity of a merry-go-round when a child moves towards the center, resulting in an increase in angular velocity due to a decrease in the system's moment of inertia.

Step-by-step explanation:

The question provided is a physics problem requiring an understanding of the conservation of angular momentum to determine the change in angular velocity of a merry-go-round when one of the children on it moves to the center. Angular momentum is conserved when no external torques act on a system. As a result, when the 28.0 kg child moves to the center, the moment of inertia of the system decreases, causing the angular velocity to increase to conserve angular momentum since angular momentum (L) is the product of the moment of inertia (I) and the angular velocity (ω), and is given by L = Iω.

Step-by-step Explanation:

Initial angular momentum (Linitial) is the product of the initial moment of inertia (Iinitial) and the initial angular velocity (ωinitial).When the child moves to the center, the new moment of inertia (Inew) is less than the initial moment of inertia.Since angular momentum is conserved, Linitial = Lnew, which means Iinitialωinitial = Inewωnew.Solve for the new angular velocity (ωnew) using the equation, which will be higher due to the reduction in moment of inertia.